Video: The Acceleration of Gravity: Definition & Formula

In this lesson, we will introduce the acceleration due to gravity. Objects in free fall are one of the few real world examples of straight line motion with constant acceleration, so they are commonly used when learning kinematics.

Angela has taught college Microbiology and has a doctoral degree in Microbiology.

In this lesson, we will introduce the acceleration due to gravity. Objects in free fall are one of the few real world examples of straight line motion with constant acceleration, so they are commonly used when learning kinematics.

Observing Kinematics

This is one of my favorite concepts in kinematics. Before we get too far, I want you to fully grasp what we're dealing with today. Look around and pick up the first thing you see. Now, stretch your arm out and drop it. It fell, right? Awesome. Now pick up whatever you dropped, and we'll continue. For those of you who decided to drop your phone, tablet, or computer monitor on your hardwood floors, you might have trouble finishing this lesson. The rest of us, let's begin our kinematic look at the acceleration due to gravity.

Gravity and Free Fall

Throughout kinematics, we have to make a lot of rules. When you're just beginning to learn kinematics, we have to set limitations and ignore forces and variables that make our lives unpredictable. One method is to focus in on objects moving in a straight line with constant acceleration. Can you even think of an instance in the real world where this happens? Your car doesn't accelerate constantly. You walk, run and drive around curves. But, pick that object up again. If you hold it at the same height and drop it one more time, it should travel straight down to the floor. Sounds like straight-line motion to me. It should also start motionless, speed up from the force of gravity alone, and be traveling pretty close to the same speed when it hits the floor every single time you drop it. That sounds like constant acceleration to me.

Today, I'm going to introduce you to the topics of free fall and the acceleration due to gravity. Free fall describes any motion involving a dropped object that is only acted on by gravity and no other forces.

Gravity is the natural mutual attraction between physical bodies. Gravity is a very complex issue. Much too complex to dive too deeply here, so I'll simplify it a bit. The earth is attracted to you just like you are attracted to the earth. But, the earth has a mass much, much greater than yours. That's why when you jump, you fall back to the earth instead of the earth visibly rising up to you. Close to the surface of the earth, the magnitude of this attraction is constant, and one way to measure it is how fast you accelerate back down after jumping up.

I need to pause here briefly to impose one limitation. I know. Sorry about this, but it wouldn't be physics without at least one. Pull out a flat sheet of paper and a pencil. If you drop them at the same time from the same height, I'm betting the pencil lands first. This difference is because of the air resistance on each object. The large surface area of the paper has to move much more air out of the way than the thin pencil as they fall. As a result, the pencil accelerates much faster than the paper. If we remove the air, though, the two objects would fall at exactly the same rate. We need to do just that when studying free fall. When doing free fall problems, you can ignore the impacts of air resistance. Now, the only force we're dealing with is gravity. Without the impacts of air resistance, all objects will accelerate at the same rate and will land at the same time if dropped from the same height.

The Acceleration Due to Gravity

The magnitude of the acceleration due to gravity, denoted with a lower case g, is 9.8 m/s^2.

g = 9.8 m/s^2

This means that every second an object is in free fall, gravity will cause the velocity of the object to increase 9.8 m/s.

For most exams, you'll need to memorize this number. Questions might even ask you to calculate velocity or displacement of an object in free fall, and never even mention gravity, acceleration, or the value of g. You're going to have to remember you have this information already. You should always assume 9.8 m/s^2, unless the question supplies you with a different acceleration, like if an object is dropped on the moon, for example.

To tackle these types of problems, you might also have to make a couple of other assumptions. If an object is dropped, you can assume the initial velocity is 0 m/s. You can also call the initial position of a dropped object 0 m. Of course, if the problem supplies you with these values, use what you're given.

Gravity Vector

Recall that acceleration is a vector quantity, meaning it has a magnitude and direction. With free fall problems, the vector is always pointing downwards. Gravity can only act downwards even if the object is moving up, like a baseball thrown straight up. The motion of the ball is up, but gravity is pulling downward on that ball, slowing its velocity.

It's most common to assume that anything moving up has a positive vector, while anything moving downward has a negative vector. This is the most common way to set up these problems and the way you'll likely see your exam questions set up. If you keep this in mind and always stick to this convention, it will keep you from getting the wrong vector sign, even though you did the math correctly.

Remember when I told you that g = 9.8 m/s^2? Well, we need to adjust that a little bit considering this new information. If we are sticking with down being negative, and gravity can only act downwards, then the acceleration due to gravity has to be negative as well. This makes our new relationship:

g = -9.8 m/s^2

Lesson Summary

Let's briefly review the concepts of free fall and the acceleration due to gravity.

Free fall in kinematics involves investigating the effects of gravity on a falling object, while ignoring the effects of air resistance. Gravity always acts to pull an object downward. It's best to stick to the most common convention that objects moving up have a positive vector, while objects falling down have a negative vector. This makes the acceleration due to gravity:

g = -9.8 m/s^2

Learning Outcomes

After you've completed this lesson, you should be able to:

Describe what free falling objects are

Explain gravity's relationship to objects in free fall

Summarize why the acceleration due to gravity is represented by a negative number

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